Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems

Zhou, Tianxiao

doi:10.1090/S0025-5718-03-01473-X

Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems
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Math. Comp. 72 (2003), 1655-1673 Request permission

Abstract:

How, in a discretized model, to utilize the duality and complementarity of two saddle point variational principles is considered in the paper. A homology family of optimality conditions, different from the conventional saddle point conditions of the domain-decomposed Hellinger–Reissner principle, is derived to enhance stability of hybrid finite element schemes. Based on this, a stabilized hybrid method is presented by associating element-interior displacement with an element-boundary one in a nonconforming manner. In addition, energy compatibility of strain-enriched displacements with respect to stress terms is introduced to circumvent Poisson-locking.

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